# Re: up to some resource bound

```On 2/16/2012 7:27 PM, Stephen P. King wrote:
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```On 2/16/2012 7:09 PM, acw wrote:
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```Do you understand at all the stuff about material and idea monism that I
have mentioned previously? We are exploring the implications of a very
sophisticate form of Ideal Monism that I am very much interested in, as
it has, among other wonderful things, an unassailable proof that
material monism is WRONG. What I am trying to discuss is how this is a
good thing but the ontological theory as a whole that it is embedded in
has a problem that is being either a) misunderstood, b) ignored or both.
```
To be fair, I still have trouble understanding your objections to UDA 8/MGA, and this discussion has been going on for quite some time now, maybe I'm just incapable of seeing the subtle distinction that you're trying to draw. Bruno postulates arithmetic or combinators, but if you want a different ontological foundation, you can formulate it and see how it fits within COMP (in case you assume it) and how that changes predictions and/or explanations.
`Hi ACW,`
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My objection to UDA 8/MGA is that it assumes something that is is deeply problematic. There is a difference between Computational universality, in the sense of any given recursively enumerable algorithm is universal if it does not depend for its functional properties on a particular physical implementation of it, and the ideas that Recursively Enumerable Algorithms (REA) have properties and "run" completely independent of the possibility of implementation in physical hardware.
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```
My proof is mathematical but may be very poorly explained because I have a very hard time translating my thoughts into words and for this I apologize. I am hoping that you can see past the words and "grok" the meaning. I am identifying the invariant aspect of a REA with a fixed point in a manifold of transformations where the "points" that make up the manifold represent the physical systems capable of implementing the REA and then applying Brouwer's Fixed point theorem:
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How can Brouwer's fixed point theorem be applied computers of REAs, they don't form a manifold.
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```here is an example for Wiki.
In the plane <http://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem>

"Every continuous
<http://en.wikipedia.org/wiki/Continuous_function_%28topology%29>
function /f/ from a closed <http://en.wikipedia.org/wiki/Closed_set> disk
<http://en.wikipedia.org/wiki/Disk_%28mathematics%29> to itself has at
least one
fixed point."

```
Think about this: Does the fixed point continue to exist if the collection of points making up that closed disc or the continuous transformations that are the functions where to vanish? Answer: No. The same way a computation is no longer a computation in the sense of universality when there is no "universe" for it.
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The point is that unless it is possible for a physical system to implement a REA, there is no such thing as an REA.
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That's the crux of the disagreement. Bruno says 2 exists because it's the successor of the successor of zero. I think it exists as a concept because we invented it, along with counting (c.f. "The Origin of Reason" by William S. Cooper). But I'm willing to take it's existence, along with the rest of arithmetic, as an hypothesis just to see where it leads.
```
Brent

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So all the talk of computations or whatever is taken as equivalent vanishes into meaninglessness when and if we jump to the conclusion that USA/MGA "proves" that the physical world is just a epiphenomenon of numbers. That is the problem.
```
Onward!

Stephen

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